As an alternative to \(\Psi ^\dagger \)  we introduce here a stable reconstructor \(\Psi \)  of (REF ).
A common choice is the Tikhonov regularized reconstructor [1]}, [2]}, defined as:
\(\Psi ^{\lambda , L}(y^\delta ) = \arg \min _{x \in \mathbb {R}^{n}} \frac{1}{2} || Ax - y^\delta ||^2 + \frac{\lambda }{2} || Lx ||^2\) 
